Related papers: The Renormalization Group According to Balaban - I…
The main theme of the paper is the detailed discussion of the renormalization of the quantum field theory comprising two interacting scalar fields. The potential of the model is the fourth-order homogeneous polynomial of the fields,…
Renormalization group method is one of the most powerful tool to obtain approximate solutions to differential equations. We apply the renormalization group method to Hamiltonian systems whose integrable parts linearly depend on action…
Quantum renormalization group scheme provides a microscopic understanding of holography through a general mapping between the beta functions of underlying quantum field theories and the holographic actions in the bulk. We show that the…
We develop the functional renormalization group formalism for a tensorial group field theory with closure constraint, in the case of an Abelian just renormalizable model with quartic interactions. The method allows us to obtain a closed but…
In this thesis we investigate aspects of two problems. In the first part of this thesis, we concentrate on renormalization group methods in Hamiltonian framework. We show that the well-known coupled-cluster many-body theory techniques can…
I study a class of interacting conformal field theories and conformal windows in three dimensions, formulated using the Parisi large-N approach and a modified dimensional-regularization technique. Bosons are associated with composite…
The paper is an attempt to relate two vast areas of the applicability of the renormalization group (RG): field theoretic models and partial differential equations. It is shown that the Green function of a nonlinear diffusion equation can be…
Renormalization group methods are applied to a scalar field within a finite, nonlocal quantum field theory formulated perturbatively in Euclidean momentum space. It is demonstrated that the triviality problem in scalar field theory, the…
We employ the machinery of smooth scaling and coarse-graining of observables, developed recently by us in the context of so-called fluctuation operators (inspired by prior work of Verbeure et al) to make a rigorous renormalisation group…
We derive a set of rotationally covariant amplitude equations for use in multiscale simulation of the two dimensional phase field crystal (PFC) model by a variety of renormalization group (RG) methods. We show that the presence of a…
We consider a possibility to unify the methods of regularization, such as the renormalization group method, stochastic quantization etc., by the extension of the standard field theory of the square-integrable functions $\phi(b)\in…
The one-dimensional Hubbard model with different on-site interactions is investigated by renormalization group technique. In the case of a 1/4-filled band the dynamical nonequivalence of sites leads to the appearance of Umklapp processes in…
A renormalization group theory for a system consisting of coupled superconducting layers as a model for typical high-temperature superconducters is developed. In a first step the electromagnetic interaction over infinitely many layers is…
We report recent progress on the application of the tensor renormalization group (TRG) to quantum field theories pursued by the Tsukuba group. We explain how to treat the scalar, fermion, and gauge theories with the TRG method presenting…
We formulate the standard real-space renormalization group method in a way which takes into account the correlation between blocks. This is achieved in a dynamical way by means of operators which reflect the influence on a given block of…
We develop a method for treating a series of secularly growing terms obtained from quantum perturbative calculations: autonomous first-order differential equations are constructed such that they reproduce this series to the given order. The…
We consider a class of toy models describing a fermion field coupled with a boson field. The model can be viewed as a Yukawa model but with scalar fermions. As in our first paper, the interaction kernels are assumed bounded in the fermionic…
We show that general cutoff scalar field theories in four dimensions are perturbatively renormalizable through the use of diagrammatic techniques and an adapted BPH renormalization method. Weinberg's convergence theorem is used to show that…
We extend the method of differential renormalization to massive quantum field theories treating in particular $\ph4$-theory and QED. As in the massless case, the method proves to be simple and powerful, and we are able to find, in…
I give an outline of recent applications of the renormalisation group to effective theories of nuclear forces, focussing on the use of a Wilsonian approach to analyse systems of two or three nonrelativistic particles.